#### Answer

{18}

#### Work Step by Step

25 - 6x = -83
Step 1: Subtract 25 from both the sides
25 - 6x = -83 -25
Step 2: Simplify
-6x = -108
Step 3: Divide both the sides by -6
$\frac{-6x}{-6}$ = $\frac{-108}{-6}$
Step 4: Simplify
x = 18
Now we check the proposed solution, 18, by replacing x with 18 in the original equation.
Step 1: the original equation 25 -6x = -83
Step2: Substitute 18 for x
25 - 6.(18) = -83
Step 3: Multiply 6.(18) = 108
25 - 108 = -83
Step 4: Solve 25 - 108= -83
-83 =- 83
Since the check results in true statement, we conclude that the solution set of the given equation is {18}